NIT

It is tough for you to get an admission but don't lose hope. Please regularly visit the official website for cutoffs and maybe you can get the admission, so don't worry.

Yes sure, you are eligible for JEE Advanced exam. Now you have to secure good marks in JEE Advanced paper to secure a seat in any IITs. So prepare hard for JEE Advanced and practice a lot of questions as much as you can do and do not lose hope.

Hello Lavi,
It's totally dependent on your category because if you are from general category then it's a no. If you are from OBC-NCL then also still no. If you are from SC/ST, you can get a low ranked NIT with a civil branch. If you are from PWD, then yes in any NIT or IIIT of your choice with your favorite branch.

You cannot get any NIT. You should go for private engineering or government engineering colleges either through state counselling or direct admission process. Many of private engineering colleges provide best placements like Nirma University, LPU, Chandigarh University, JECRC, Amity University, Arya College Jaipur, Poornima College Jaipur, etc.

ECE is the best as most demanded in the modern era. This is second top branch after CS which is highly growing.

Since the cutoff of CSE branch is more than other branches so to get it in NIT is not possible but you could take any other branches to get into NITs and if you'll work hard in first year then you'll definitely be upgraded to higher branches like CSE based on your performance.

You may get till last round of counselling.

Hello,
I hope you are doing well. Yes definitely you can definitely get any IIIT or NIT with your 5K ranking of JEE Mains. For your reference I am attaching a link where you can find the list of NIT and IIIT you will get based on your ranking:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=connect&utm_medium=CR_JEECP&utm_campaign=7489993

Fill IIST's form before 5 junk and you will definitely get that college. You can go for ISCR too and do counselling till last round so you can get IIT, Dhanbad too.

https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor
Please follow the above mentioned link.